1. Field of the Invention
The invention relates to a dynamically variable lens made of an electromagnetic metamaterial. The invention also relates to a method of dynamically varying a metamaterial lens. The invention also relates to a resonance frequency tunable system.
2. Discussion of the Related Art
Lenses that operate on the visible range of the radiation spectrum are typically made of glass or plastic. Lenses made of these materials are very effective over most of the visible range. However, these materials display a small dependence on frequency or wavelength, noticed as chromatic aberration. Chromatic aberration is corrected in compound lens systems. A limited number of special lens materials are effective in the infrared range. Materials effective for terahertz range optical elements are more limited and reflective optics are often used instead of refractive lenses because of absorption effects.
Lenses can be fabricated from arrays of metallic or dielectric discs for the radio wave to microwave range. A refractive lens made from arrays of discs which operates in the short radio wave range is shown in Optics, 2nd Edition by Eugene Hecht, p. 136 (Addison-Wesley, Reading, Mass.), incorporated herein by reference. Lenses that operate in the microwave regime can also be made of dielectric polymer materials such as Rexolite®, or Marcors®. These materials are effective over a fairly broad band; however, their use is limited because a fabricated lens is large, heavy and limited by geometry to fixed focal lengths. Other artificial dielectrics have been developed for microwave lenses, but they are typically limited in bandwidth.
Lenses made of negative refractive index (NIM) metamaterials have been demonstrated in the microwave range. A first type of lens is a plano-concave lens with a negative refractive index. This is shown in C. G. Parazzoli et al., Applied Physics Letters 84, 3232-3234 (2004), incorporated herein by reference. The lens has a refractive index of n=−1.31 at 14.7 GHz, a focal length of 5.19 cm and a radius of curvature of 12 cm. The concave lens and negative index combination acts like a convex, positive index lens. Parazzolli et al. teach that for a NIM lens to have the same focal length as a positive index lens, the NIM lens employs a larger radius of curvature, which reduces lens aberrations. Unwanted lens surface reflections can be reduced in a metamaterial lens by fitting the outer surface of the lens impedance to match that of free space. NIM lenses can have a weight advantage of a factor of approximately 10 over standard dielectric positive index lenses.
A second type of lens made of NIM material is a gradient-index or GRIN lens. The lens effect is achieved by varying the index of refraction as a function of radial position from the center of the lens. This is distinguished from a lens with a constant index of refraction material in which the thickness of the lens varies from the center to the outer edge. Negative index GRIN lenses are demonstrated by R. B. Greegor et al., Applied Physics Letters 87, 091114 (2005) and by T. Driscoll et al., Applied Physics Letters 88, 081101 (2006). Both are incorporated herein by reference.
The R. B. Greegor et al. reference shows in FIG. 1 a comparison of a GRIN lens, a plano-concave NIM lens, and a conventional positive index cylindrical piano-convex lens. T. Driscoll et al. designed and fabricated a biplanar, or geometrically flat, lens with a radially varying index gradient with the distribution as a function of radius at a point r for a lens of diameter d, described in the equation:
                              ɛ          ⁡                      (                          r              ,              ω                        )                          =                              μ            ⁡                          (                              r                ,                ω                            )                                =                      η            (                          r              ,                              w0                =                                                      -                    0.97                                    -                                      7.30                    ⁢                                                                  (                                                  r                          /                          d                                                )                                            2                                                        +                                      0.18                    ⁢                                                                  (                                                  r                          /                          d                                                )                                            4                                                                                  ,                                                          Eq        .                                  ⁢                  (          1          )                    wherein: ∈ is the permittivity, μ is the magnetic permeability, and n is the negative index of refraction, each a function of angular frequency ω. The first equality in Eq. (1) ensures impedance matching and therefore no reflection at the surface of the lens. The prescribed radial distribution was achieved at a frequency of 10.1 GHz. Lens diameter was 30 centimeters.
The radial distributions indicated in Eq. (1) were achieved by assembling an array of metamaterial unit cells. Each unit cell is a metamaterial split ring resonator (SRR) and wire, shaped to have a specific magnetic and electric resonance. The lens was given a radial gradient by radially positioning 50 incrementally different unit cells. The disc shaped lens produced contains one layer of metamaterial consisting of 8,000 unit cells. Approximately one-quarter of the cells were unitary, i.e. unique. Lenses constructed of both eight layers and four layers of this material were tested and shown to focus microwave radiation at 10.3 GHz, only 2% different from the design frequency. The above-cited T. Driscoll et al. reference illustrates the structure of one layer of the GRIN lens. FIG. 1 shows the split ring resonator (SRR) and wires (straps) which make up a unit cell. FIG. 1 also illustrates the array of SRRs inside a single layer of the lens.
The metamaterial NIM lenses of the prior art are only capable of operating in a very narrow band centered on a single frequency. They have a fixed focal length at the operating frequency. They do have a significant advantage over standard dielectric lenses in that they can be approximately 10 times lighter for microwave applications. They also can be designed to occupy less space than conventional lenses. This can be important for aerospace communications applications where weight and volume are of particular concern. Another advantage of NIM lenses is reduced aberration.
Inventors have discovered that problems and deficiencies associated with known lenses and materials of construction therefor can be solved or greatly reduced by the use of a dynamically variable metamaterial lens.